Blender Internal texture not influencing geometry
You are probably missing a UV map. I did a simple "standard cube" setup to help you better debug what is missing or not working (here I used blender render for a quick setup):



After creating the texture as you said in question, I also got rendered a flat standard cube, but then I created a simple "smart UV project" umap, using all defaults, and just this made the influence to appear in rendering results.

A UV map is needed because your texture must be "mapped" to the mesh surface, and the UV map is how you tell about your desired surface mapping.

hth